%0 Journal Article %T Some results on pre-monotone operators %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Alizadeh, M.H. %A Roohi, M. %D 2017 %\ 11/30/2017 %V 43 %N 6 %P 2085-2097 %! Some results on pre-monotone operators %K Generalized monotone operators‎ %K ‎upper semicontinuous‎ %K ‎convex function‎ %R %X ‎In this paper‎, ‎some properties of pre-monotone operators are proved‎. ‎It is shown that in a reflexive Banach space‎, ‎a full domain multivalued $\sigma$-monotone operator with sequentially norm$\times$weak$^*$ closed graph is norm$\times$weak$^*$ upper semicontinuous‎. ‎The notion of $\sigma$-convexity is introduced and the‎ ‎relations between the $\sigma$-monotonicity and $\sigma$-convexity is investigated‎. ‎Moreover‎, ‎some results on the sum and difference of two $\sigma$-monotone operators is considered. %U http://bims.iranjournals.ir/article_1085_cc4d2b57b686d6c39e4e826525d95114.pdf